I replaced the belt in an MDS-JB980 this evening. I had intended to follow 2many's method but it became clear to me quite quickly that I was going to struggle with that (you might have more success if you're more dexterous than I am, have some more suitable tools and you are not in need of new reading glasses...) so I ended up following kgallen's method (using one of my daughter's hairpins to re-affix the spring).
There's a video of someone replacing the belt in an MDS-JE780 here:
It looks very similar to the MDS-JB980 inside, although one of the earth leads is connected differently.
In fact, when I had my MDS-JB980s open earlier I noticed that a number of the circuit boards were labelled "Sony MDS-JE780" and a couple of others "Sony MDS-JB940". Sony obviously used the same parts in a number of their decks.